Book Reviews

The book Signature of the Spheres by Hartmut Warm explores the figures made by the planets in their courses, with some beautiful coloured illustrations and supported by many apt quotations from eminent writers. The pentagon revealed by Venus after many orbits is a well known example, but in this book more complex and fascinating ‘signatures’ are investigated. Of special interest and importance is the work on Johannes Kepler’s harmonies of the spheres. What has been regarded conventionally as wishful thinking by Kepler is shown to have a genuine and profound basis. The reader will need some mathematical ability to follow the arguments in detail, but the text is readable and interesting in its own right.

The book begins with a review of the history of astronomy since about 1600AD when the old Ptolemaic theory of the planets was gradually overturned, principally by Galileo, Kepler, Tycho Brahe and Sir Isaac Newton. The modern theories based on perturbed elliptic orbits are thoroughly explained with illustrations. Early on the question is raised: how far can individuals claim to have gained any spiritual stability from the discoveries of modern astronomy? We now have an abundance of precise and detailed measurements of the way the planets move to enable us to assess whether ‘there’s not the smallest orb but in his motion like an angel sings’ or whether ‘… all [is] in pieces, all coherence gone; All just supply, and all Relation …’. To this end various ratios between the observable properties of the planets are introduced, for the ‘signatures’ are thus uncovered in relation to beautiful geometrical forms. These relate remarkably to musical intervals. The first typical ‘signature’ diagram presented is of the forms made by the positions of the conjunctions of Jupiter and Saturn, followed by diagrams illustrating musical relationships of the various planets.

There follows a critical look at the modern theories of the origin of the universe compared with various creation myths, and the Platonic musical scale. A detailed description of Kepler’s work follows, particularly his search for a musical basis for the Solar System. Kepler eventually arrived at ratios of perihelion to aphelion of neighbouring pairs of planets (on the orbit of a planet ‘perihelion’ is the point of closest approach to the Sun, ‘aphelion’ the point furthest from the Sun) and of perihelion to perihelion and aphelion to aphelion, gaining thereby – with the exception of Jupiter to Mars – a plausible musical (major) scale. The effect of more accurate modern data makes only a minimal difference to his results. Kepler’s discovery of two wonderful geometric ‘stars’ follows.

The ‘harmony of the spheres’ claimed to have been heard consciously by Pythagoras, and in dream by others, is suggestive but generally uncheckable. It is necessary to asses how far musical correspondences, including intervals and chords, could arise by chance. This is undertaken more rigorously than by previous investigators, possibly for the fi rst time. The initial result arrived at for Kepler’s scale – based on an assumed fundamental note and restricted to the 11 neighbouring intervals – is disappointing, being only about 90% statistically signifi cant, or nearer to 80% when the three planets discovered since his day are included.

Hartmut Warm proceeds to a wider analysis using all ratios, not just those of neighbouring planets, and finds remakable results. First of all the intervals based on the velocity at perihelion conform to a musical scale with a probabilty of that arising by chance of 0.000130, i.e. less than 0.1%. Then he fi nds that the ratios of the velocities at aphelion to when the planet is separated from the Sun by its semi-minor axis distance yield a scale with a probability by chance of 0.00000096%. This extension of Kepler’s intuition is truly remarkable!

The musical structure of the Solar System is established with ‘astronomical’ (sic!) probabilities. The statistical method employed seems rigorous and convincing. The rest of the book is delightful, and the mathematics rigorous and pictures beautiful, but this must surely be its summit, lending credence to ‘there’s not the smallest orb but in his motion like an angel sings’. Next, what amounts to the ‘Goldilocks paradox’ is discussed, i.e. how come all the physical constants and laws are ‘just right’ for the evolution of life, and of us? This is judged to be nothing less than a ‘miracle’ [those

who are comfortable with it as ‘chance’, or invoke parallel universes (at enormous energy-expense) remind one of Christ’s observation ”… they strain at a gnat but swallow a camel”!]. A more comprehensive assessment of modern cosmology appears towards the end of the book. Are stars, it is asked, with their ‘life cycles’ not unlike living beings? What right have we to deride this? The distribution of our Solar System planets, and their speed of formation based on current theories, suggest to Hartmut Warm that a proposal by other authors of waves in the primordial dust cloud could be interpreted as a ‘music of the spheres’ underlying the creation process. Then the reason for a musical scale in the Solar System could be understood. Hans Jenny’s work is cited in support, which showed how Chladni-like interacting vibrations could produce similar structures.

A review of the impact of modern chaos theory on the stability or otherwise of the Solar System concludes that it is unlikely to be of real signifi cance. Then many diagrams are derived showing the striking geometric figures produced by relationships between pairs of planets, all illustrating further long term rhythms of varied kinds. Some involve three planets in a neat way e.g. the positions of Mercury when Venus and Mars are in conjunction. The resonances involved seem to contribute to the overall long-term stability of the Solar System. The study of the geometrical forms. e.g. lying behind aphelion and perihelion ratios, is cited as an approach to the unknown spiritual source of the planetary music.

There follow studies of remarkable fi gures arising from the relationships between, e.g., Venus, Earth and Mars, showing the role of the cross and the pentagram in the movements of the inner Solar System. Then figures related to the rotations of the planets on their axes are studied, with the striking result that whole-number relationships arise repeatedly despite the fact that the numbers defi ning the orbital elements are essentially incommensurable. ‘A Symphony of fl owers and stars’ is exhibited in the harmonious interplay of the inner and outer planetary systems. A critical assessment of modern cosmology ensues and then an excursion into particle physics. Once more a musical relationship arises, now between particle masses and lifetimes, with a probability of 1 in 2000 that it is mere chance.

In his further assessment Hartmut Warm says ”So our world cannot have come into being by accident; either it has always existed or it is a divine creation”, based on the unavoidable (and materialistically unpalatable) assumptions that must be made if the universe had a beginning. The book concludes by showing how relations between the semiminor axes can be exhibited by squares, based on a pentagonal underpinning, to a very high degree of accuracy. Kepler’s geometrical ‘stars’ are also included. This is a tour-de-force by Hartmut Warm involving an imaginative approach in relation both to geometry and music. There is much more in the book than can be covered in a brief review.

All the above provide further pointers to the spiritual underpinning of the creation. It can always be argued, of course, that if you search far enough patterns will emerge by chance, but the diversity and beauty of those uncovered in this book suggests otherwise to those who are not ‘tone-deaf’. Hartmut Warm ends by expressing his appreciation to the Creator.

The ancient Greeks believed not only that the Cosmos has order to it but that this order is musical, expressed as a harmony of the spheres in the orderly progression of the planets. As our understanding os astronomy and cosmic laws has developed, our need for an idea of harmonious has not, laments Hartmut Warm, a German civil engineer and independent researcher.

In the note to this English edition he asserts that while Pluto has been demoted from planet status, it is still very much part of “the community of the planets”: it sings in geometric harmony with the movements of the entire solar system.

Warm’s diagrams representing geometrical and harmonic basics as well as correspondences between musical and planetary ratios are a joy to behold, and his explanations and supporting charts add gravitas to his argument. Warm concludes that this cosmic harmony is evident in each planet’s relationship with each other and the solar system as a whole. His colour diagrams of planetary relationships, e.g. Venus-Earth linklines are spectacular. They demonstrate a “symphony of flowers and stars” and perfect celestial harmony, according to Warm’s description in his brilliat analysis.